Columbia University Patent and FinDer Software System
Columbia University now holds patents for:
Portfolio structuring using low discrepancy sequences.
US Patent 5,940,810, was issued on August 17, 1999, to Joseph F. Traub, Spassimir Paskov, and Irwin Vanderhoof, and has been assigned to Columbia University where the work was conducted.
US Patent 6058377, was issued on May 2, 2000, to Joseph F. Traub, Spassimir Paskov, Irwin Vanderhoof, and Anargyros Papageorgiou, and has been assigned to Columbia where the work was conducted.
The discovery
Columbia has patented a method for valuing a complex security using samples derived from points belonging to a low discrepancy sequence, whenever the security value is represented by an integral in at least fifty dimensions. It has also patented a method for portfolio structuring, where the potential loss and the Value-at-Risk are calculated using a low discrepancy sequence.
Contrary to the opinion of the leading experts in the early 90’s, we discovered that low discrepancy methods, also called quasi-Monte Carlo methods, when applied to valuation of complex securities (which includes financial derivatives as an important special case), are far superior to Monte Carlo in three ways
- They are faster by a factor of 10 to 1000
- They are more accurate
- Monte Carlo is very sensitive to the initial seed
Scientific impact
After the publication of our discoveries there has been a huge increase of research in the area. RISK books published a volume of papers on Monte Carlo and Quasi-Monte Carlo (Dupire, 1998). There has been an explosion in the number of conferences. Publications of the Columbia group include Paskov and Traub, 1995, Papageorgiou and Traub, 1996, Paskov, 1997, Sloan and Wozniakowski, 1998, Papageorgiou and Paskov, 1999. We have reported progress at many RISK conferences (London, New York, Chicago) and spoken at numerous university colloquia. Additional tests, publications and other information are given on the FinDer section of this site (see also ~ap.)
We have given free academic licenses to over 40 researchers. Prior to the issuance of the patent, a number of people told us that they could not replicate our excellent results using publicly available software. We have made improvements in the Sobol’ sequence and, since the filing date of the patent, improvements in the generalized Faure low discrepancy sequence in FinDer.
A novel application of a mathematical method
As is well known, mathematics cannot be patented. What Columbia has patented is a novel application of a mathematical method to finance using a computer to produce a useful tangible result.
The study of low discrepancy sequences is part of number theory. There are numerous instances of discoveries regarding the application of mathematics to technology being patented. One important example is the use of number theory to create secure cryptographic codes.
Disclosure of advances
Article 1, Section 8, Clause 8 of the United States Constitution gives Congress the power “[t]o promote the progress of science and the useful arts by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries.” The Federal patent system encourages the creation and disclosure of new, useful, and non-obvious advances in the useful arts. The ultimate goal is to bring new technologies into the public domain through disclosure.
Columbia University will license the FinDer software system or the patent for commercial use under reasonable terms and conditions. The moneys are used to conduct further research of interest to the financial community.
Partial list of Columbia Publications
1. Paskov, S., and Traub, J.F. (1995) “Faster Evaluation of Financial Derivatives”, The Journal of Portfolio Management, 22(1), 113-120.
2. Papageorgiou, A., and Traub, J.F. (1996) “Beating Monte Carlo”, RISK, June, 63-65.
3. Paskov, S. (1997) “New Methodologies for Valuing Derivatives”, in Mathematics For Derivative Securities, S. Pliska and M. Dempster eds., Isaac Newton Institute, Cambridge University Press, UK, 545-582.
4. Sloan, I.H., and Wozniakowski, H. (1998) “When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?”, J. Complexity, 14, 1-33.
5. Papageorgiou, A., and Paskov, S. (1999) “Deterministic Simulation for Risk Management”, The Journal of Portfolio Management, May, 122-127.